Problem: First consider the expression for: Take the product of $7$ and $x$ and add $3$. Now select the answer that matches the following: The sum of $-5$ and the product of $-7$ and that expression.
Answer: Let's break this problem into smaller and easier pieces. What is the product of $7$ and $x$ $7 \times x = \color{orange}{7x}$ What does adding $3$ to $7x$ do? $7x$ $ + 3$ What is the quantity of $-7$ times that expression $-7 \times (7x + 3) = \color{orange}{-7(7x+3)}$ What is the sum of $-5$ and $\color{orange}{-7(7x+3)}$ $-7(7x+3)$ $ - 5$ So the entire expression we're considering can be written as $-7(7x+3)-5$.